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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Evaluate the Graph
• Give a verbal description of the motion • Rank in order the speeds at points A, B, and C, from
slowest to fastest. • Draw a velocity-versus-time graph (including the correct
numerical scale)
B
A C
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Evaluate Graphs
• For each graph, answer the following question. • Do A and B ever have the same speed? If so, at what
time or times?
B
A B A
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Motion Activity
• Use a motion detector with the LoggerQuest • Motion Activity - One member of each group walks • at a steady speed away from the motion detector • at a steady speed toward the motion detector • at an increasing speed away from the motion detector • at a decreasing speed away from the motion detector • at an increasing speed toward the motion detector • at a decreasing speed toward the motion detector
• For each, sketch diagrams, position graphs, and velocity graphs
• To change time, switch modes so that the choices are File and Sensor, then select Data Collection
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Tactics: Interpreting position-versus-time graphs
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Finding Position from Velocity If we know the initial position, si, and the instantaneous velocity, vs, as a function of time, t, then the final position is given by
Or, graphically;
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Back and Forth
acceleration
velocity
position
acceleration
velocity
position
derivative
derivative
integral
integral
area
area
slope
slope
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 2.7 The displacement during a drag race
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Find Area Graphically
• Using the graph, find the position at t = 1, 2, 3, 4, and 5 s and make a table.
• From this data, draw a position-versus-time graph
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Find Area Graphically
• A train is moving at a steady 30 m/s. At t = 0s, the engine passes a single light at x = 0 m. Without using any formulas, find the engine’s position at t = 1 s, t = 2 s and t = 3 s.
• Graph position and velocity versus time • Find the area from the velocity-versus-time graph
• Δs = area under the velocity-versus-time graph
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Position-Versus-Time
• Trucker Bob starts the day 120 miles west of Denver. He drives east for 3 hours at a steady 60 miles/hour before stopping for his coffee break.
• Draw a position-versus-time graph for Bob, including appropriate numerical scales along both axes.
• Let Denver be located at x = 0 and assume that the x-axis points to the east.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Uniform Motion
Straight-line motion in which equal displacements occur during any successive equal-time intervals is called uniform motion. For one-dimensional motion, average velocity is given by
Notice the symbol Δ. It represents a displacement and an interval in time - not position or instant in time
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Problem Solving Strategy
• Sally opens her parachute at an altitude of 1500 m. She then descends slowly to earth at a steady speed of 5 m/s. How long does it take her to touch down?
• Draw pictorial representation – coordinates, symbols • Motion diagram • Mathematical Representation • Are results reasonable?
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
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